Variational optimization algorithms for uniform matrix product states

2017/01/31 by Valentin Zauner-Stauber, V. Zauner-Stauber, L. Vanderstraeten +7 · 281 citations
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Convergence (economics) #Decimation #Density matrix #Density matrix renormalization group #Filter (signal processing) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Matrix product state #Physics #Physics of Superconductivity and Magnetism #Product (mathematics) #Quantum #Quantum many-body systems #Quantum mechanics #Renormalization group #Spectroscopy and Quantum Chemical Studies #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.97.045145

published in Physical review. B./Physical review. B 97(4) (American Physical Society) · 20 pages + 12 pages appendix, V. Zauner-Stauber previously also published under the name V. Zauner

openalex publication_date 2018/01/25 · arxiv created 2019/04/19 · arxiv updated 2019/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

Citations

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